A1209
Title: Consistent estimation of the number of clusters in multi-layer and dynamic stochastic block models
Authors: Lucie Arts - Sorbonne Universite – LPSM (France) [presenting]
Abstract: Clustering in networks aims at grouping nodes into communities, and a key challenge is estimating the number of clusters. Stochastic Block Models (SBMs) provide a probabilistic framework for such networks, and the Krichevsky-Trofimov (KT) estimator has been shown to consistently recover the number of clusters in single SBMs. This approach is extended to collections of graphs on the same set of nodes, including multilayer (MLSBM) and dynamic (DynSBM) SBMs. In MLSBMs, nodes share a latent structure across layers, with assignments independent across layers, while in DynSBMs, node groups evolve over time according to independent, stationary, irreducible, aperiodic Markov chains. In both Models, edges are conditionally independent given node groups and follow Bernoulli distributions parameterized by group interactions. A penalized KT estimator is defined as the maximizer of the integrated likelihood minus a model-dependent penalty over the number of clusters. The estimator is shown to be consistent as the number of nodes increases, providing a principled method for selecting the number of clusters in collections of networks and enabling reliable analysis of multilayer and temporal network structures.
